ON THE POLYGONAL AND CIRCULAR REPRESENTATIONS OF THE (123) – AVOIDING PETTERNS OF AUNU PERMUTATION NUMBERS
DOI:
https://doi.org/10.33003/fjs-2026-1004-4321Keywords:
AUNU Permutation Patterns, Cayley Tables, Polygonal Representation, Circular Representation, Non-associative/non-commutativity PropertyAbstract
In this communication, another theoretic Property of the (123) - Avoiding class of AUNU permutation patterns is x-rayed. Here, we consider the Polygonal and Circular representations as studied by Paulus Gerdes of these patterns with a view of exploring more of their pictorial applications in relation to interconnection Networks, e.t.c. Our results are obtained by the consideration of the Cayley tables of these patterns used by Ibrahim and Abubakar to study their Non-associativity/non-commutativity of . Our goal is achieved by considering these Patterns for where n is prime. The polygonal and circular Representation of these patterns are thus obtained with the aim of giving some graphical network structures.
References
Chun B. Pamson (2025) A [ 7 4 2 ] Linear Code due to the Cayley table for n = 7 for the Generated points of the (123)/(132) - Avoiding Patternsof the Non- Associative AUNU Schemes, International Journal of Development Mathemathics. Vol 2 issue 4 Pp 131-136
Chun P.B (2018). On Algebraic Theoretic Properties of the "(123)/(132)"- avoiding class of AUNU Permutation pattern: Applications in code generation and analysis. PhD Thesis, Usmanu Danfodiyo University, Sokoto.
Chun, P. B, Ibrahim, A.A, Garba, A.I (2016b). Algebraic Theoretic Properties of the Non-associative Class of (132)-Avoiding Patterns of AUNU Permutations: Applications in the Generation and Analysis of a General Cyclic Code. Computer Science and Information Technology, 4 ,45 - 47. doi: 10.13189/csit.2016.040201.
Chun P.B, Ibrahim A.A, and Garba A.I, (2016a) Algebraic theoretic properties of the avoiding class of AUNU permutation patterns: Application in the generation and analysis of linear codes. International Organization for Scientific Research (IOSR), Journal of Mathematics12(1) pp 1-3.
Ibrahim A.A., and Abubakar S.I. (2016a) Non-Associative Property of 123-Avoiding Class of Aunu Permutation Patterns. Advances in Pure Mathematics, 6, 51-57. http://dx.doi.org/10.4236/apm.2016.62006
Ibrahim (A.A. (2006)). Some Graph theoretical properties of (132) avoiding patterns of certain class Nigerian Journal of renewable energy 14 21 24.
Ibrahim, A.A. and Abubakar, S.I. (2016b) AUNU Integer Sequence as Non-associative Structure and their Graph theoretic properties. Advances in Pure Mathematics, 6, 409-419.
http://dx.doi.org/10.4236/apm.2016.66028
Paulus Gerdes (2007). Adventures in the World of Matrices: Nova Science publishers, Inc. New York. (chapter 34, pg 187).
Van Steen, M. (2010) An Introduction to Graph Theory and Complex Networks. Amsterdam
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Copyright (c) 2026 Bentse Pamson Chun, Charlse Shaldam Adidi, Philip Terwase Ajai

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